The hamiltonian-formalism tag has no wiki summary.
6
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9answers
2k views
Book about classical mechanics
I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
7
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3answers
2k views
When is the Hamiltonian of a system not equal to its total energy?
I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
13
votes
1answer
181 views
Sympletic structure of General Relativity
Inspired by physics.SE: http://physics.stackexchange.com/questions/15571/does-the-dimensionality-of-phase-space-go-up-as-the-universe-expands/15613
It made me wonder about symplectic structures in ...
9
votes
5answers
1k views
Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?
When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics.
Now when we studied QM, on the level of Griffiths, we ...
4
votes
2answers
257 views
Hamiltonian mechanics and special relativity?
Is there a relativistic version of Hamiltonian mechanics? If so, how is it formulated (what are the main equations and the form of Hamiltonian)? Is it a common framework, if not then why?
It would be ...
5
votes
3answers
441 views
How does one quantize the phase-space semiclassically?
Often, when people give talks about semiclassical theories they are very shady about how quantization actually works.
Usually they start with talking about a partition of $\hbar$-cells then end up ...
4
votes
2answers
356 views
Energy operator
Does the Hamiltonian always translate to the energy of a system? What about in QM? So by the Schrodinger equation, is it true then that $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ ...
4
votes
3answers
565 views
Why is the symplectic manifold version of Hamiltonian mechanics used in Newtonian mechanics?
Books such as Mathematical methods of classical mechanics describe an approach to classical (Newtonian/Galilean) mechanics where Hamiltonian mechanics turn into a theory of symplectic forms on ...
2
votes
1answer
157 views
Find the Hamiltonian given $\dot p$ and $\dot q$
I have these equations:
$$\dot p=ap+bq,$$
$$\dot q=cp+dq,$$
and I have to find the conditions such as the equations are canonical. Then, I have to find the Hamiltonian $H$.
To answer to the first ...
9
votes
2answers
257 views
Hamiltonian or not?
Is there a way to know if a system described by a known equation of motion admits a Hamiltonian function? Take for example
$$ \dot \vartheta_i = \omega_i + J\sum_j \sin(\vartheta_j-\vartheta_i)$$
...
3
votes
4answers
588 views
Lagrangian to Hamiltonian in Quantum Field Theory
While deriving Hamiltonian from Lagrangian density, we use the formula
$$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$
But since we are considering space and time as parameters, why the formula
...
2
votes
3answers
129 views
Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?
An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
5
votes
2answers
161 views
Weyl Ordering Rule
While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian ...
4
votes
3answers
181 views
What are some mechanics examples with a globally non-generic symplecic structure?
In the framework of statistical mechanics, in books and lectures when the fundamentals are stated, i.e. phase space, Hamiltons equation, the density etc., phase space seems usually be assumed to be ...
4
votes
2answers
868 views
Lagrangian mechanics vs Hamiltonian mechanics
First of all, what are the differences between these two: Lagrangian mechanics and Hamiltonian mechanics?
And secondly, do I need to learn both in order to study quantum mechanics and quantum field ...
3
votes
3answers
364 views
Type of stationary point in Hamilton's principle
In this question it is discussed why by Hamilton's principle the action integral must be stationary. Most examples deal with the case that the action integral is minimal: this makes sense - we all ...
2
votes
2answers
305 views
Correct application of Laplacian Operator
Not a physicist, and I'm having trouble understanding how to apply the Laplacian-like operator described in this paper and the original. We let:
$$ \hat{f}(x) = f(x) + \frac{\int H(x,y)\psi(y) ...
1
vote
3answers
189 views
Factors of $c$ in the Hamiltonian for a charged particle in electromagnetic field
I've been looking for the Hamiltonian of a charged particle in an electromagnetic field, and I've found two slightly different expressions, which are as follows:
$$H=\frac{1}{2m}(\vec{p}-q \vec{A})^2 ...
5
votes
4answers
218 views
Non-Integrable systems
Integrable systems are systems which have $2n-1$ time-independent, functionally independent conserved quantities (n being the number of degrees of freedom), or n whose Poisson brackets with each other ...
3
votes
3answers
199 views
Writing $\dot{q}$ in terms of $p$ in the Hamiltonian formulation
In the Hamiltonian formulation, we make a Legendre transformation of the Lagrangian and it should be written in terms of the coordinates $q$ and momentum $p$. Can we always write $dq/dt$ in terms of ...
2
votes
1answer
52 views
Hamiltonian of polymer chain
I'm reading up on classical mechanics. In my book there is an example of a simple classical polymer model, which consists of N point particles that are connected by nearest neighbor harmonic ...
